If a and b are positive integers such that a/4b = 6.35, which of the following could be the remainder when 4a is divided by 2b?

If a and b are positive integers such that a/4b = 6.35, which of the following could be the remainder when 4a is divided by 2b?

• A. 16
• B. 32
• C. 40
• D. 64

Answer: (C)

To find the remainder when \(4a\) is divided by \(2b\), we start from the given equation \( \frac{a}{4b} = 6.35 \). Rearranging, we have: \[ a = 6.35 \times 4b = 25.4b \] Since \(a\) and \(b\) are both positive integers, \(b\) must be chosen such that \(25.4b\) is also an integer. This is only possible if \(b\) is a multiple of \(10\) because \(25.4\) can be expressed as \( \frac{254}{10} \). Therefore, \(b\) can take values like \(10, 20, 30, \ldots\). Next, we can express \(4a\): \[ 4a = 4(25.4b) = 101.6b \] Now, we need to divide \(4a\) by \(2b\): \[ 2b = 2b \] Now, let’s divide \(4a\) by \(2b\): \[ \frac{4a

To find the remainder when (4a) is divided by (2b), we start from the given equation ( \frac{a}{4b} = 6.35 ). Rearranging, we have:

[

a = 6.35 \times 4b = 25.4b

]

Since (a) and (b) are both positive integers, (b) must be chosen such that (25.4b) is also an integer. This is only possible if (b) is a multiple of (10) because (25.4) can be expressed as ( \frac{254}{10} ). Therefore, (b) can take values like (10, 20, 30, \ldots).

Next, we can express (4a):

[

4a = 4(25.4b) = 101.6b

]

Now, we need to divide (4a) by (2b):

[

2b = 2b

]

Now, let’s divide (4a) by (2b):

[

\frac{4a